# What is the vertex of y=-(x-4)(x+4)?

Dec 12, 2015

Vertex: $\left(0 , 16\right)$

#### Explanation:

You are given the equation in a factor form. By setting both factors to zero you know the two roots.
$x - 4 = 0$

$x = 4$

$x + 4 = 0$

$x = - 4$

The vertex is always exactly in between those two points so you can find where x is

$x = \frac{- 4 + 4}{2}$

$x = 0$
You can see that if you graph the equation
graph{-(x-4)(x+4) [-57, 57, -28.5, 28.5]}

Now that you have x, just plug that into the equation and solve for y

$y = - \left(0 - 4\right) \left(0 + 4\right)$

$y = - \left(- 4\right) \left(4\right)$

$y = - \left(- 16\right)$

$y = 16$

So the vertex is $\left(0 , 16\right)$